The situation illustrated in the following block diagram occurs frequently when a digital computer is used to control a continuous system. The digital computer is modeled as a pure time delay of T seconds. The continuous system is a simple integrator. Use the root locus magnitude condition to find the maximum time delay such that the system remains stable.
Hint: Use a Pade approximation to represent the time delay as a rational transfer function and substitute
What will be an ideal response?
The time delay is approximated using first order Pade approximation,
The forward loop transfer function becomes,
The transfer function is manipulated into “root locus form” by solving,
The root locus plot is shown below,
At K=0.93, the closed loop poles are at and the system becomes unstable as K falls below this value and for negative values as well (the CRL). This K value can also be derived from the root locus magnitude condition,
For the system to be stable,
You might also like to view...
About 60 percent of the ducks raised in the United States are raised on Long Island, New York
Indicate whether the statement is true or false.
This is a list that identifies each part in the assembly and correlates the parts to the assembly. This list is usually on the assembly print but can be separate.
a. parts list b. list of materials c. description of parts d. description of materials
E85 means that the fuel is made from ________
A) 85% gasoline, 15% ethanol B) Ethanol that has 15% water C) 85% ethanol, 15% gasoline D) Pure ethyl alcohol
In specifying a plug or slot weld, if the depth of filling is required, it is shown in inches or millimeters and the dimension is placed ____.
A. within B. above C. to the left of D. to the right of